I first reviewed two main methods of estimating seismic attenuation: ray-based tomography and the wave-equation-based method. Then I presented a new method for estimating Q, which uses central frequency shift to analyze Q versus offset (QVO) or Q versus angle (QVA). Based on this proposed method, I developed theories for estimation of Q in both data space and image space, and applied them to a 2D synthetic model. I also presented Q migration and Q compensation methods based on one-way wave equation. Our results showed that Q compensation recovers the amplitude loss caused by attenuation, which is a successful step forward for image-based Q estimation.